Models For Binary Data Research Articles

Regression of binary network data with exchangeable latent errors

AbstractUndirected, binary network data consist of indicators of symmetric relations between pairs of actors. Regression models of such data allow for the estimation of effects of exogenous covariates on the network and for prediction of unobserved data. Ideally, estimators of the regression parameters should account for the inherent dependencies among relations in the network that involve the same actor. To account for such dependencies, researchers have developed a host of latent variable network models; however, estimation of many latent variable network models is computationally onerous and which model is best to base inference upon may not be clear. We propose the probit exchangeable (PX) model for undirected binary network data that is based on an assumption of exchangeability, which is common to many of the latent variable network models in the literature. The PX model can represent the first two moments of any exchangeable network model. We leverage the EM algorithm to obtain an approximate maximum likelihood estimator of the PX model that is extremely computationally efficient. Using simulation studies, we demonstrate the improvement in estimation of regression coefficients of the proposed model over existing latent variable network models. In an analysis of purchases of politically aligned books, we demonstrate political polarization in purchase behavior and show that the proposed estimator significantly reduces runtime relative to estimators of latent variable network models, while maintaining predictive performance.

MSR80 A Dynamic Panel Binary Data Model for Personalized Patient Engagement Prediction

Recently, pharmaceutical companies offer “nurse ambassadors” to assist patients continuing the use of medications, however, the patient engagement is one of the main issues during treatment. To investigate the impact of in-person or virtual assistance and better engage patients, we develop a dynamic panel binary data model to forecast the patients’ engaged probability at a future time point.

Zero-inflated probit Bernoulli model: a new model for binary data

This study proposes a new model in the family zero-inflated (ZI) binary models, it is called as a ZI Probit Bernoulli (ZIPBer) model. This model can be performed to model or simulate binary data that has an excessive amount of zero counts. At the framework of this research, we first introduce the classical formula, estimating equation (EE) and related functions for the ZIPBer model. Next, the results of asymptotic inferences for the ZIPBer model is studied based on the widespread regularity conditions. For the numerical illustrations, many simulation studies and a practical data set are executed in this paper. Specifically, we perform the fishing data set (FDS) to check the working effectiveness and robustness of the maximum likelihood estimation (MLE) approach in estimating parameters for the ZIPBer model. We also illustrate that this actual data set is more suitable for the proposed model: ZIPBer than other binary models such as logit, probit and ZIBer. The achieved results in this study are very unanimous with reality. It also illustrates that this is a dependable verification for us to know the solution as well as how to proceed to how to catch or take the most fish. This is the contribution of this work in terms of application. Finally, some crucial discussions and conclusions are given in this paper.

Inverse Probability Weighting Estimation in Completely Randomized Experiments

In addition to treatment assignments and observed outcomes, covariate information is often available prior to randomization in completely randomized experiments that compare an active treatment versus control. The analysis of covariance (ANCOVA) method is commonly applied to adjust for baseline covariates in order to improve precision. We focus on making propensity score-based adjustment to covariates under the completely randomized design in a finite population of experimental units with two treatment groups. We study inverse probability weighting (IPW) estimation of the finite-population average treatment effect for a general class of working propensity score models, which includes generalized linear models for binary data. We provide randomization-based asymptotic analysis of the propensity score approach and explore the finite-population asymptotic behaviors of two IPW estimators of the average treatment effect. We identify a condition under which propensity score-based covariate adjustment is asymptotically equivalent to an ANCOVA-based covariate adjustment and improves precision compared with a simple unadjusted comparison between treatment and control arms. In particular, when the working propensity score is fitted by a generalized linear model for binary data with an intercept term, the asymptotic variance of the IPW estimators is the same for any link function, including identity link, logit link, probit link, and complementary log-log link. We demonstrate these methods using an HIV clinical trial and a post-traumatic stress disorder study. Finally, we present a simulation study comparing the finite-sample performance of IPW and other methods for both continuous and binary outcomes. Supplementary materials for this article are available online.

25 Hydroxyvitamin D Serum Concentration and COVID-19 Severity and Outcome-A Retrospective Survey in a Romanian Hospital.

Interest in the immunomodulatory function of vitamin D has grown since the COVID-19 pandemic started. Our study investigated the possible association between vitamin D deficiency and COVID-19 severity, intensive care needs, and mortality in patients hospitalized with COVID-19. A prospective cohort study was performed on 2342 COVID-19 hospitalized patients between April 2020 and May 2022 in a Romanian tertiary hospital for infectious diseases. A multivariate generalized linear model for binary data was fit with dependent variables: severe/critical form of COVID-19, intensive care need, and fatal outcome as a function of vitamin D deficiency, controlling for age, comorbidities, and vaccination status. More than half of the patients (50.9%) were classified with vitamin D deficiency based on a serum concentration of less than 20 ng/mL. There was a negative association between vitamin D and age. Vitamin D-deficient patients presented with more cardiovascular, neurological, and pulmonary diseases, as well as diabetes, and cancer. In multivariate logistic regression models, vitamin D-deficient patients had higher odds of severe/critical forms of COVID-19 [OR = 1.23 (95% CI 1.03-1.47), p = 0.023] and higher odds of death [OR = 1.49 (95% CI 1.06-2.08), p = 0.02]. Vitamin D deficiency was associated with disease severity and death outcome in hospitalized COVID-19 patients.

Heywood Cases in Unidimensional Factor Models and Item Response Models for Binary Data.

Heywood cases are known from linear factor analysis literature as variables with communalities larger than 1.00, and in present day factor models, the problem also shows in negative residual variances. For binary data, factor models for ordinal data can be applied with either delta parameterization or theta parametrization. The former is more common than the latter and can yield Heywood cases when limited information estimation is used. The same problem shows up as non convergence cases in theta parameterized factor models and as extremely large discriminations in item response theory (IRT) models. In this study, we explain why the same problem appears in different forms depending on the method of analysis. We first discuss this issue using equations and then illustrate our conclusions using a small simulation study, where all three methods, delta and theta parameterized ordinal factor models (with estimation based on polychoric correlations and thresholds) and an IRT model (with full information estimation), are used to analyze the same datasets. The results generalize across WLS, WLSMV, and ULS estimators for the factor models for ordinal data. Finally, we analyze real data with the same three approaches. The results of the simulation study and the analysis of real data confirm the theoretical conclusions.

A Latent Shrinkage Position Model for Binary and Count Network Data

A Latent Shrinkage Position Model for Binary and Count Network Data

Bayesian Analysis of First-Order Markov Models for Autocorrelated Binary Responses.

In many clinical trials, patient outcomes are often binary-valued which are measured asynchronously over time across various dose levels. To account for autocorrelation among such longitudinally observed outcomes, a first-order Markov model for binary data is developed. Moreover, to account for the asynchronously observed time points, nonhomogeneous models for the transition probabilities are proposed. The transition probabilities are modeled using B-spline basis functions after suitable transformations. Additionally, if the underlying dose-response curve is assumed to be non-decreasing, our model allows for the estimation of any underlying non-decreasing curve based on suitably constructed prior distributions. We also extended our model to the mixed effect model to incorporate individual-specific random effects. Numerical comparisons with traditional models are provided based on simulated data sets, and also practical applications are illustrated using real data sets.

A Double-Penalized Estimator to Combat Separation and Multicollinearity in Logistic Regression

When developing prediction models for small or sparse binary data with many highly correlated covariates, logistic regression often encounters separation or multicollinearity problems, resulting serious bias and even the nonexistence of standard maximum likelihood estimates. The combination of separation and multicollinearity makes the task of logistic regression more difficult, and a few studies addressed separation and multicollinearity simultaneously. In this paper, we propose a double-penalized method called lFRE to combat separation and multicollinearity in logistic regression. lFRE combines the logF-type penalty with the ridge penalty. The results indicate that compared with other penalty methods, lFRE can not only effectively remove bias from predicted probabilities but also provide the minimum mean squared prediction error. Aside from that, a real dataset is also employed to test the performance of the lFRE algorithm compared with several existing methods. The result shows that lFRE has strong competitiveness compared with them and can be used as an alternative algorithm in logistic regression to solve separation and multicollinearity problems.

An adjusted scale binomial Beta H-Likelihood estimation method for unbalanced clustered

In practice, clustered binary responses are very prevalent, where binary data is naturally grouped by sampling techniques. Clusters are often unequal in size in some areas of studies, such as medicine, education and others. The most suitable models for binary data clusters of unbalanced sizes are the Hierarchical Generalized Linear Model (HGLM), where the random term over-dispersion counts; and it is k known as clustered binary data. Current techniques for estimating parameters in (HGLM) are many, but these techniques do not allow over dispersion to be distinct from cluster to cluster. Where clustered binary data resulted in over-variation, that reasonable to conclude the unequal size of clustered binary data may have been distinct variations for distinct clusters. By ignoring the chance of shifting over variability between clusters, test statistics may be inflated in the Type I error rates. In this paper, the binomial beta (BB) (HGLM) method has been altered to account for distinct variations across separate clusters. In order to explore whether the Adjusted Scale Binomial Beta (ASBB) method is more suitable than the (BB) technique for dealing with over-dispersion for unequal cluster binary data models, the author was used simulation, the adjusted method was compared to the original "existing" technique in terms of, Type I error rate, estimator standard errors and power. (ASBB) h-likelihood “adjusted” method was comparable to BB "existing" technique, as it has a less standard error and the Type I error was acceptable. Moreover, Type I error inflated in “exist method” (BB) h-likelihood.

On Hierarchical Bayesian Spatial Small Area Model for Binary Data under Spatial Misalignment

Small area models have become popular methods for producing reliable estimates for sub-populations (small geographic areas in this study). Small area modeling may be carried out via model-assisted approaches within the model-based approaches or design-based paradigm. When there are medium or large samples, a model-assisted approach may be reliable. However, when data are scarce, a model-based technique may be required. Model-based Bayesian analysis is popular for its ability to combine information from several sources as well as taking account uncertainties in the analysis and spatial prediction of spatial data. Nevertheless, things become more complex when the geographic boundaries of interest are misaligned. Some authors have addressed the problem of misalignment under hierarchical Bayesian approach. In this study, we developed non-trivial extension of existing hierarchical Bayesian model for a binary outcome variable under spatial misalignment with three contributions. First, the model uses unit-level survey data and area-level auxiliary data to predict the posterior mean proportion spatially at the second geographic area level. Second, the linking model is changed to logit-normal model in the proposed model. Lastly, the mean process was considered to overcome the multicollinearity between the true predictors and the spatial random effect. Sensitivity analysis was also done via simulation.

Zero-inflated generalized extreme value regression model for binary response data and application in health study

ABSTRACT Binary responses are often present in medical studies. When the dependent variable Y represents a rare event, the logistic regression model shows relevant drawbacks. To overcome these drawbacks, we propose the quantile function of the generalized extreme value regression distribution as a link function and focus our attention on values close to one. One problem arising in the presence of cure fraction is that, it is usually unknown who are the cured and the susceptible subjects, unless the outcome of interest has been observed. In these settings, a logistic regression analysis is no more straightforward. We develop a maximum likelihood estimation procedure, based on the joint modeling of the binary response of interest and the cure status. We investigate the identifiability of the resulting model and establish the asymptotic properties. We conduct a simulation study to investigate its finite-sample behaviour, and application to real data.

Modeling a smooth course of learning and testing individual deviations from a global course

Formative assessment supplies valuable feedback for teachers and learners, and has been facilitated by computerized implementations. While longitudinal within-student assessment or within-class comparisons are useful, a normative interpretation of an individual’s course of learning can only be given relative to a reference population. As current computerized assessment systems sample items from pools or adapt tests, monitored students might work on non-overlapping item sets, so that classic sum scores cannot be compared directly. To meet this challenge, the Smooth Growth and Linear Deviations Rasch Model (SGLDRM) is introduced, an extension of Rasch’s item response theory model for binary test data. With the help of spline functions a smooth global course of learning is included. The model is flexible enough to accommodate increases and/or decreases of the mean ability level, which might be more or less pronounced at each measurement occasion. On the individual level, a random slope and a random intercept with amenable interpretations modify the global course of learning. Two measurement occasions suffice to estimate person-specific courses. A likelihood ratio test allows identifying students whose performance differs from the mean course. The methodology is illustrated with data from an online dyscalculia assessment and training.

Contagion effects of UK small business failures: A spatial hierarchical autoregressive model for binary data

This article focuses on modelling the contagion effects - both between and within groups - on small business failures in London. Small business clusters can be defined based on different companies’ characteristics, for example, economic sector or geographical location. These aspects are usually included as fixed effects to predict the defaults of small- and medium-sized enterprises (SMEs). However, this approach however ignores the interactions between the company groups and only captures the heterogeneity across the clusters. To include both contagion effects between and within groups, a Bayesian spatial hierarchical model for binary data is proposed and applied to a dataset of SMEs located in London in 2016. The empirical analysis shows that the contagion component at the lower level, based on the geographical location, is not significant if the industry clustering is ignored. However, it becomes significant if the industry group effect is included, and also the upper-level interdependence also becomes significant. Finally, the suggested model improves the predictive accuracy and the expected shortfall estimate compared to standard scoring models.

Space-time modeling of intensive binary time series eye-tracking data using a generalized additive logistic regression model.

Eye-tracking has emerged as a popular method for empirical studies of cognitive processes across multiple substantive research areas. Eye-tracking systems are capable of automatically generating fixation-location data over time at high temporal resolution. Often, the researcher obtains a binary measure of whether or not, at each point in time, the participant is fixating on a critical interest area or object in the real world or in a computerized display. Eye-tracking data are characterized by spatial-temporal correlations and random variability, driven by multiple fine-grained observations taken over small time intervals (e.g., every 10 ms). Ignoring these data complexities leads to biased inferences for the covariates of interest such as experimental condition effects. This article presents a novel application of a generalized additive logistic regression model for intensive binary time series eye-tracking data from a between- and within-subjects experimental design. The model is formulated as a generalized additive mixed model (GAMM) and implemented in the mgcv R package. The generalized additive logistic regression model was illustrated using an empirical data set aimed at understanding the accommodation of regional accents in spoken language processing. Accuracy of parameter estimates and the importance of modeling the spatial-temporal correlations in detecting the experimental condition effects were shown in conditions similar to our empirical data set via a simulation study. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Simultaneous confidence bands in a zero-inflated regression model for binary data

Abstract The logistic regression model has become a standard tool to investigate the relationship between a binary outcome and a set of potential predictors. When analyzing binary data, it often arises, however, that the observed proportion of zeros is greater than expected under the postulated logistic model. Zero-inflated binomial (ZIB) models have been developed to fit binary data that contain too many zeros. Maximum likelihood estimators in these models have been proposed, and their asymptotic properties were recently established. In this paper, we use these asymptotic properties to construct simultaneous confidence bands for the probability of a positive outcome in a ZIB regression model. Simultaneous confidence bands are especially attractive since they allow inference to be made over the whole regressor space. We construct two types of confidence bands, based on: (i) the Scheffé method for the linear regression model; (ii) Monte Carlo simulations to approximate the distribution of the supremum of a Gaussian field indexed by the regressor. The finite-samples properties of these two types of bands are investigated and compared in a simulation study.

Scalable Computation of Predictive Probabilities in Probit Models with Gaussian Process Priors

Predictive models for binary data are fundamental in various fields, and the growing complexity of modern applications has motivated several flexible specifications for modeling the relationship between the observed predictors and the binary responses. A widely-implemented solution is to express the probability parameter via a probit mapping of a Gaussian process indexed by predictors. However, unlike for continuous settings, there is a lack of closed-form results for predictive distributions in binary models with Gaussian process priors. Markov chain Monte Carlo methods and approximation strategies provide common solutions to this problem, but state-of-the-art algorithms are either computationally intractable or inaccurate in moderate-to-high dimensions. In this article, we aim to cover this gap by deriving closed-form expressions for the predictive probabilities in probit Gaussian processes that rely either on cumulative distribution functions of multivariate Gaussians or on functionals of multivariate truncated normals. To evaluate these quantities we develop novel scalable solutions based on tile-low-rank Monte Carlo methods for computing multivariate Gaussian probabilities, and on mean-field variational approximations of multivariate truncated normals. Closed-form expressions for the marginal likelihood and for the posterior distribution of the Gaussian process are also discussed. As shown in simulated and real-world empirical studies, the proposed methods scale to dimensions where state-of-the-art solutions are impractical.

Maximum likelihood estimation in the generalized extreme value regression model for binary data

Generalized extreme value regression model is widely used when the dependent variable Y represents a rare event. The quantile function of the GEV distribution is used as link function to investigate the relationship between the binary outcome Y and a set of potential predictors X. In this article we develop a maximum likelihood estimation procedure int he generalized extreme value regression model. We establish the asymptotic properties (existence, consistency and asymptotic normality) of the proposed maximum likelihood estimator.

Constructing Flexible, Identifiable and Interpretable Statistical Models for Binary Data

SummaryBinary regression models are ubiquitous in virtually every scientific field. Frequently, traditional generalised linear models fail to capture the variability in the probability surface that gives rise to the binary observations, and remedial methods are required. This has generated a substantial literature composed of binary regression models motivated by various applications. We describe an organisation of generalisations to traditional binary regression methods based on the familiar three‐part structure of generalised linear models (random component, systematic component and link function). This perspective facilitates both the comparison of existing approaches and the development of flexible models with interpretable parameters that capture application‐specific data‐generating mechanisms. We use our proposed organisational structure to discuss concerns with certain existing models for binary data based on quantile regression. We then use the framework to develop and compare several binary regression models tailored to occupancy data for European red squirrels (Sciurus vulgaris).

SCClone: Accurate Clustering of Tumor Single-Cell DNA Sequencing Data.

Single-cell DNA sequencing (scDNA-seq) enables high-resolution profiling of genetic diversity among single cells and is especially useful for deciphering the intra-tumor heterogeneity and evolutionary history of tumor. Specific technical issues such as allele dropout, false-positive errors, and doublets make scDNA-seq data incomplete and error-prone, giving rise to a severe challenge of accurately inferring clonal architecture of tumor. To effectively address these issues, we introduce a new computational method called SCClone for reasoning subclones from single nucleotide variation (SNV) data of single cells. Specifically, SCClone leverages a probability mixture model for binary data to cluster single cells into distinct subclones. To accurately decipher underlying clonal composition, a novel model selection scheme based on inter-cluster variance is employed to find the optimal number of subclones. Extensive evaluations on various simulated datasets suggest SCClone has strong robustness against different technical noises in scDNA-seq data and achieves better performance than the state-of-the-art methods in reasoning clonal composition. Further evaluations of SCClone on three real scDNA-seq datasets show that it can effectively find the underlying subclones from severely disturbed data. The SCClone software is freely available at https://github.com/qasimyu/scclone.